Plot before Interpolation

The color gradient indicates the amount of rainfall, with darker shades representing higher precipitation and lighter shades indicating lower rainfall. Based on the map, it appears that:Northern area receives the highest amount of rainfall, with a significant portion of the region receiving over 750 cm of annual rainfall. Southern area experiences considerably lower rainfall, with many areas receiving less than 250 cm per year. The coastal region receives moderate rainfall, with annual precipitation typically ranging between 250 and 500 cm.

IDW with power 0

[inverse distance weighted interpolation]

The IDW interpolation with a power of 0 is very smooth and gives the mean annual rainfall for all areas

IDW with power 1

[inverse distance weighted interpolation]

the IDW interpolation with a power of 1 offers a more informative representation of the predicted annual rainfall than power zero which shows that all areas have the same amount of annual rainfall. The map shows most of the areas received an annual rainfall above 300cm. The map though smooth reveals gradual changes in rainfall intensity across the region, with gradients from wetter areas in the north to drier areas in the south.

IDW with power 2

[inverse distance weighted interpolation]

The IDW interpolation with a power of 2 exhibits less smoothness and reveals distinct trends compared to the interpolation with power 1. In the southern region, areas now appear darker, indicating annual rainfall levels below 200 cm, which suggests a decrease in rainfall compared to the power 1 interpolation. While the northern areas continue to receive more rainfall, the amounts are still lower than those predicted with power 1. Notably, the regions experiencing the highest annual rainfall are concentrated in the north westernmost areas which agrees with the orginal data as the points in those areas were very light. The tip of the south gets less more than 400cm annual rainfall rain than the tip of the north

CROSS-VALIDTION

[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]
[inverse distance weighted interpolation]

  IDW..power...0. IDW..power...1. IDW..power...2.
1        166.3445        127.5178         85.0365

The IDW results for the different power coefficients show distinct variations in estimated annual rainfall. For a power of 0, the average rainfall estimate is 166.34 cm, which indicates that the interpolation is uniform across the area, treating all points equally without considering their distance. As the power increases to 1, the average estimate drops to 127.52 cm, reflecting a moderate weighting of nearby points over those further away. Finally, at a power of 2, the average estimate further decreases to 85.04 cm, suggesting that the interpolation is heavily influenced by the nearest points, resulting in a more localized and potentially less smooth surface.

Bubble Plots for IDW with power=0

[inverse distance weighted interpolation]

The points along the line are shaded darker, indicating they are farther from a residual of zero. Additionally, many points are located well above and below the line, suggesting the model tends to underestimate higher rainfall values and overestimate lower ones. This highlights areas where the model’s predictions diverge significantly from the actual data.

Bubble plot for IDW power=1

[inverse distance weighted interpolation]

The points are mostly scattered around the diagonal line, indicating that the predicted annual rainfall values are generally close to the observed values.The color of the dots on the line indicates that the residual are close to zero which indicates that model predicts annual rainfall well.However, few points are located farther away from the diagonal line indicating larger differences between predicted and observed values.The residual range from -200 to 200 which is different from the range of the residuals of the model with power 0

Bubble plot for IDW with power=2

[inverse distance weighted interpolation]

For the IDW interpolation with a power of 2, most points along the diagonal are shaded like the shades around zero, indicating that their residuals are close to zero, which suggests the model is performing well in predicting annual rainfall. However, there are a few points that deviate from the line. The lightly shaded points below the line indicate the model is underestimating rainfall in those areas, while the darker points above the line show overestimation. Most of these points are still very close to the diagonal, meaning the deviations are relatively small, overall reflecting a good model fit.The range for the residuals for this model is 100 points less than that of the model with power 0 and 1

Before Interpolation

Interpolation

[using ordinary kriging]

Kriggin Cross Validation

[using ordinary kriging]
[using ordinary kriging]
[using ordinary kriging]
[using ordinary kriging]
[using ordinary kriging]

      RMSE
1 64.85976

RMSE= 64.9cm which is less than the RMSE of the IDW with different powers.